What are the different methods to calculate the distance between two points on a coordinate plane?
There are several methods to calculate the distance between two points on a coordinate plane. One commonly used method is the distance formula, which is derived from the Pythagorean theorem.
Here are the steps to calculate the distance:
1. Identify the coordinates of the two points. Let's say the coordinates of Point A are (x1, y1) and the coordinates of Point B are (x2, y2).
2. Use the distance formula:
Distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]
3. Subtract the x-coordinates (x2 - x1) and square it.
(x2 - x1)^2
4. Subtract the y-coordinates (y2 - y1) and square it.
(y2 - y1)^2
5. Add the squared values from steps 3 and 4.
[(x2 - x1)^2 + (y2 - y1)^2]
6. Take the square root of the sum obtained in step 5.
Distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]
Another way to calculate the distance is by using the Manhattan distance formula, also known as the taxicab distance or L1 norm. This method involves adding the absolute differences between the x-coordinates and y-coordinates of the two points, respectively.
Here are the steps to calculate the Manhattan distance:
1. Identify the coordinates of the two points as (x1, y1) and (x2, y2).
2. Calculate the absolute difference between the x-coordinates.
|x2 - x1|
3. Calculate the absolute difference between the y-coordinates.
|y2 - y1|
4. Add the absolute differences obtained in steps 2 and 3.
|x2 - x1| + |y2 - y1|
Using these methods, you can easily calculate the distance between any two points on a coordinate plane.